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Properties

Label 1870.2.cb
Level $1870$
Weight $2$
Character orbit 1870.cb
Rep. character $\chi_{1870}(489,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $864$
Sturm bound $648$

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Defining parameters

Level: \( N \) \(=\) \( 1870 = 2 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1870.cb (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 935 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(648\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1870, [\chi])\).

Total New Old
Modular forms 2656 864 1792
Cusp forms 2528 864 1664
Eisenstein series 128 0 128

Trace form

\( 864 q - 216 q^{4} - 8 q^{5} + O(q^{10}) \) \( 864 q - 216 q^{4} - 8 q^{5} + 16 q^{11} - 216 q^{16} - 8 q^{20} + 128 q^{21} - 16 q^{29} - 16 q^{31} + 16 q^{34} + 16 q^{35} + 56 q^{39} - 24 q^{44} - 40 q^{45} + 8 q^{46} + 8 q^{51} + 48 q^{54} - 32 q^{55} - 136 q^{61} - 216 q^{64} - 32 q^{65} + 48 q^{69} + 112 q^{71} - 16 q^{75} + 8 q^{79} + 12 q^{80} + 72 q^{81} - 32 q^{84} - 100 q^{85} - 16 q^{86} - 16 q^{89} + 136 q^{91} + 12 q^{95} - 200 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(1870, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1870, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1870, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(935, [\chi])\)\(^{\oplus 2}\)